Characterizing Non-linear Materials

Radiant Technologies, Inc.

Characterizing Non-linear Materials

Joe T. Evans, Radiant Technologies, Inc.

January 16, 2011www.ferrodevices.com

http://www.ferrodevices.com/

Radiant Technologies, Inc.2

Presentation Outline• Introduction

• A charge model for electrical materials

• Instrumentation theory based on the charge model

• Simple components in the charge model

• A component model for non-linear capacitors

• Coupled properties

• History, testing, and automation

• Conclusion


Radiant Technologies, Inc.

• Radiant Technologies pursues the development and implementation of thin ferroelectric film technology.

– Test Equipment: Radiant supplies ferroelectric materials test equipment world-wide.

– Thin Films: Radiant fabricates integrated-scale ferroelectric capacitors for use as test references and in commercial products.


The Presenter• Joe T. Evans, Jr.

• BSEE – US Air Force Academy in 1976

• MSEE – Stanford University in1982

• Founded Krysalis Corporation and built the first fully functional CMOS FeRAM in 1987

– Holds the fundamental patent for FeRAM architecture

• Founded Radiant Technologies, Inc in 1988.


An Excellent Hysteresis Loop

• This loop is nearly “perfect”. How to perceive this device and measure all of its properties is the subject of this presentation!

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Radiant Technologies, Inc. 6

The Charge Model of Electronics• Every electronic device consists of electrons and protons

powerfully attracted into self-cancelling, self-organized structures.

• Every electrical device, when stimulated by one of six changes in thermodynamic state, changes its charge state.

• Every device may be modeled as a charge source controlled by an external factor separated by infinite impedance.

Change in thermodynamic

state

Change in Polarization

Device


The Charge Model of Electronics• The infinite input impedance of the model means that the input

and output are independent of each other, coupled only by the equation describing the model.

• Consequently, the input circuitry from the tester to the Device Under Test (DUT) and the circuitry of the tester that measures the output of the DUT do not have to be related.

They only need a common reference for energy potential.


state


Device


The Charge Model of Electronics• The six thermodynamic state variables are

• Stress ( T )• Strain ( S )• Electric Field ( E )• Polarization ( P or D )• Temperature ( )• Entropy ( s )


state


Device


The Charge Model of Electronics• A traditional Loop Tracer varies only one state variable, Electric

Field, and measures the change in one other state variable, Polarization.

• Absolute units uncorrected for geometry drive the real world, hence the use of Voltage in place of Electric Field and Charge in place of Polarization in the figure above.

Change in Voltage

Change in Charge

Device


The Charge Model of Electronics• Modern “Polarization” testers measure charge and voltage

simultaneously so the change in more than one thermodynamic state may be measured during a test.

• The voltage input can be used to capture the output of sensors that convert a thermodynamic state to a voltage:• Displacement sensor• Thermocouple• Force sensor

Change in one thermodynamic

state

Change in multiple

thermodynamic states

Device


The Charge Model of Electronics• Modern ferroelectric testers are no longer Loop Tracers but

instead are Thermodynamic State Testers!

• The Precision Premier II measures charge and two input voltages on every test.

• In keeping with this model, all Radiant testers have an open architecture in electronics and software to allow the user to configure any stimulus/response configuration

Change in one thermodynamic

state

Change in multiple


Device


Absolute vs Indirect

• An absolute measurement counts or quantifies a material property directly in absolute physical units:• Number of electrons• Amplitude of a force

• An indirect measurement measures a defined property of a material and then uses a model to translate the results into an absolute property.


Absolute vs Indirect:Example

• An impedance meter, of which tens or hundreds of thousands have been sold, measures phase delay and amplitude change of a signal fed through the DUT and then uses impedance equations to convert the results into absolute values of capacitance and loss.

• A polarization tester stimulates a device with a fundamental quantity of nature -> voltage -> and counts another fundamental quantity of nature -> electrons -> before, during, and after the stimulus.


Absolute vs Indirect:Example

• An impedance meter measures averages.

An impedance meter appears to have low noise in its measurements but this is the result of measuring averages.

• A polarization tester measures single events.

A polarization tester does have high noise in its measurement but multiple single-event measurements can be averaged


Linear vs Non-linear• For a linear DUT, no matter how a parameter is

measured, the same result is obtained.

A linear capacitor measured by any tester and test technique will result in the same answer.

• For a non-linear DUT, a different starting point results in a different end point.

A non-linear capacitor will give different values to different testers attempting to measure the same parameter.

Both answers are correct!


Tester Circuits• In order for a proper thermodynamic state tester to adhere

to the model described above: The tester must stimulate the DUT directly with one of

the fundamental quantities of physics. The tester must directly count or quantify the

thermodynamic response of the DUT in absolute units. The tester should take advantage of the independence

of the output from the input. The tester must create a 1:1 time correlation between

the stimulus and the response. NO IMPEDANCE ALLOWED!


Stimulus• The stimulus can be any one of the six thermodynamic

variables applied in a manner so as to minimize any contributions from other variables.


Stimulus Voltage

o 10V created from operational amplifierso 200V created from low solid-state amplifierso 10kV created from external amplifiers

• 10kV is the limit due to expense and low demand.

o Voltage is created directly from software using Digital –to-Analog Converters (DACs).

Chargeo Charge source forces the charge state.


Stimulus Temperature

o Voltage or software controlled furnaceo Voltage or software controlled hot plateo The temperature may be generated directly by

command from the controller by voltage-to-temperature converter or by software communications.

o The temperature may not be controlled but instead may be measured as a parameter in an open-loop system.


Stimulus Force

o Any number of actuator types may be used, either voltage or software controlled.

o The force may be commanded or, like temperature, may be measured in an open-loop system.

Strain

o A strain stimulus requires

1) Force application (See above) plus

2) A strain measurement to capture that state during the test.


Stimulus A independent change in entropy is not contemplated

today as a stimulus.

Theoretically, a magnetic field is not a separate thermodynamic stimulus because it was unified with electric fields by James Maxwell in 1861. o Magneto-electric testing is coming from Radiant in the

near future.


Stimulus NOTE: For the four possible stimuli besides voltage

(temperature, strain, stress, and charge), the best and easiest implementation is a stimulus system that is voltage controlled so that a standard hysteresis test can be executed.

Device

Voltage

Change in multiple


Converter


Test System Diagram

Digital to Analog

Converter

Analog to Digital

Converter

HostComputer

Power Supply(±15V, 5V, 3.3V)

AWFG

Electrometeror

Ammeter

Power

Control

Sensors

Volts


The Test Circuit

•To the left is one example of a test path for a ferroelectric tester.

•This is the circuit for the Radiant EDU, a very simple tester.

•The EDU uses an integrator circuit to collect charge.

+

-

R1

R2

R3

DAC

+

-ADCY Channel

Sense Capacitor

Discharge Switch

Current Amplifier

ADCX Channel

Virtual Ground


A Different Test Circuit•This circuit uses a transimpedance amplifier to create the virtual ground.

•On both this circuit and the EDU circuit the input amplifier forces the input to remain at ground.

+-

R1

R2

R3

DAC

+

-ADCY Channel

Sense Capacitor

Current Amplifier

ADCX Channel

Virtual Ground


Mathematics• Transimpedance amplifier: [ aixACCT ]

− Measures “I”− Integrate “I” to get charge: P = I t /

Area− Plotted value P is calculated.

• Integrator: [ Radiant ]− Measures charge directly − Divide by area to get polarization− Plotted value P is measured. − Derivative yields current: J = [ Q/ t ] /

Area


The Virtual Ground• Electrons in the wire connected to the virtual ground input

move freely into or out of that node in response to outside forces.

• Since the virtual ground input has no blocking force to that movement, it has zero impedance.

• The integrator, or charge amp, counts electrons moving into or out of its input node independent of the voltage stimulus. Piezoelectric and pyroelectric response.


Simple Components in Charge Space• All electrical components can be measured in “Charge

Space”: Charge vs Volts.

• Time is not a parameter in the plot but does affects the results.

• Each component produces a particular shape in the Hysteresis Test.


Simple Components in Charge Space

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• Linear Capacitance



• Linear Resistance

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Hysteresis of Linear Resistor[ 2.5Mohm 4V 1ms ]

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• Back-to-back diodes

• A pair of Back-to-Back Diodes.


• In electrical engineering, a fundamental approach to understanding a system is to break it into components and model each component.

– Each component responds independently to the stimulus.

– The output of a component is either the input to another component or is summed with the outputs of other components to form the response of the device.

Modeling Nonlinear Capacitance


The Components• Remanent polarization• Linear small signal capacitance (dielectric constant)• Nonlinear small signal capacitance (dielectric constant)• Hysteretic small signal capacitance (remanent polarization

modulation)• Linear resistive leakage• Hysteretic resistive leakage• Electrode diode reverse-biased leakage• Electrode diode reverse-biased exponential breakdown


Linear Capacitance

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• Q = CxV where C is a constant


Non-linear Capacitance

• When the electric field begins to move atoms in the lattice, the lattice stretches, changing its spring constant. Capacitance goes down.

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• PUND: P*r - P^r = dP = Qswitched • Hysteresis: Switching - Non-switching = Remanence:

Remanent Hysteresis Calculation

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uC/v

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SwitchingDifferenceNon-Switching

Remanent Half Loop

Remanent Hysteresis


• The test may be executed in both voltage directions and the two halves joined to show the switching of the remanent polarization that takes place inside the full loop.

Remanent Hysteresis

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R em anent H ysteres is[ Type AB WHITE ]

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Unswitched - Logic 0 Switched - Logic 1 Remanent


• 1KHz 0.2V test with 182 points

Non-switching vs Switching CV

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1ms 4V CV nSW: Capacitance (nF) 1ms 4V CV SW: Capacitance (nF)


Small Signal Capacitance Polarization

• Small signal capacitance forms a hysteresis of its own.


Small Signal Capacitance Polarization

• The contribution of small signal capacitance hysteresis to the overall loop is small in this case.


Linear Resistance

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Hysteresis of Linear Resistor[ 2.5Mohm 4V 1ms ]

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Hysteresis in Leakage• Leakage in ferroelectric materials does not have to be linear.• Leakage can have its own hysteresis modulated by remanent

polarization.

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4V 1s nSW IV: Current (Amps) 4V 1s SW IV: Current (Amps)



• Back-to-back diodes

• A pair of Back-to-Back Diodes.



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N ormalized C V for 1-micron 4/20/80 PNZT[ Sensor Die ]

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Hysteresis of 1-micron 4/20/80 PNZT[ Sensor Die ]

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• The back-to-back diode effect is easily seen in every hysteresis loop.


Leakage vs CV vs Remanent Polarization

Hysteresis Parameters

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SW CV*10

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The Components• Remanent polarization• Linear small signal capacitance (dielectric constant)• Nonlinear small signal capacitance (dielectric constant)• Hysteretic small signal capacitance (remanent polarization

modulation)• Linear resistive leakage• Hysteretic resistive leakage• Electrode diode reverse-biased leakage• Electrode diode reverse-biased exponential breakdown

See the Radiant presentation “Ferroelectric Components - A Tutorial” for more detail.


Bulk Ceramics• Bulk Ceramic capacitors and thin film capacitors have

long been treated as completely different from each other.

• We have found that there is no difference so the same tests and the same models can be used for both.

• The results differ in appearance: The greater thickness of the bulk ceramics lowers the

contribution of dielectric constant charge while remanent polarization remains constant independent of thickness. Therefore, bulk ceramics have a lower slope and look more square even though they have the same properties as thin films.


Test Definitions• Hysteresis – the polarization curve due to a continuous

stimulus signal. The signal can have any shape.

• Pulse – the polarization change resulting from a single step up and step down in voltage. Essentially a 2-point hysteresis loop.

• Leakage – the current continuing to pass from or through the sample after the polarization has quit switching.

• IV – Individual leakage tests conducted over a voltage profile.


Tests• Small Signal Capacitance – The polarization response of

the sample when stimulated by a voltage change smaller than that required to move remanent polarization.

• CV – small signal capacitance measured over a voltage profile.

• Piezoelectric Displacement – the change in dimensions of the capacitor during voltage actuation. Each test listed above has its counterpart measurement of piezoelectric displacement.


Tests• Pyroelectricity– the change in charge with a change in

temperature. Remanent polarization changes or Dielectric constant changes.

• Three types of pyroelectric tests: Static: measure dielectric constant or remanent

polarization at different temperatures. Calculate slope. Roundy-Byers: ramp temperature and measure

current. Photonic: Hit sample with infrared pulse and measure

polarization change.


Tests• Magneto-electric - expose sample to changing magnetic

field while measuring polarization change.

• Ferroelectric Gate Transistor - Pulse the gate of the transistor and then measure

channel conductivity with the gate set to zero volts. Measure traditional Ids versus Vds. New measurement unique to memory transistors:

Ids versus Vgs.


• A Polytec Laser Vibrometer measuring a 1-thick Radiant PNZT film.

Piezoelectric Displacement


• The d33 for Radiant’s 1 4/20/80 PNZT ranges from approximately 60pm/V to 80pm/V.

Piezoelectric Displacement

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1u PN Z T Piston[ T y p e A C W H IT E ]

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• Execute steps in temperature, measuring remanent polarization at each step.

Static Pyroelectric

Remanent Polarization vs Temperature

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• Execute steps in temperature, measuring remanent polarization at each step.

Static Pyroelectric

Remanent Polarization vs Temperature

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Use the SYNC signal on the rear panel of the tester to open a shutter and expose the sample to IR signal.

Photonic Pyroelectric

Power Sensor

Tester

DRIVE RETURN SENSOR

SYNC

IR Source


Shutter Acquisition Example - Bulk SBT

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Shutter Open

Photonic Pyroelectric


Magneto-Electric

Precision Tester

DRIVE RETURN SENSOR1

Gauss Meter

USB to host

Helmholtz Coil


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Magnetoelectric Response vs Time

Difference

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Drive Voltage

Drive

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Radiant’s very first results working with Virginia Tech University. See upcoming paper.


Ferroelectric Gate TransistorRadiant builds transistors with thin ferroelectric film gates and developed the software to test them.

Premier II

DriveReturn

Sensor

I2C I2C DACModule

BIAS

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Ids vs V ds [ X N 5 -3 in T O -18 ]

Ids

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rre

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(A)

Volts

Ids vs Vds: 1 Ids vs Vds: 2 Ids vs Vds: 3

Ids vs Vds: 4 Ids vs Vds: 5 Ids vs Vds: 6

Vg = 0

Vg = 1V

Vg = 2VVg = 3VVg = 4VVg = 5V


Ferroelectric Gate TransistorTFF transistors require some tests that are different.

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Switching vs Non-sw itching Ids vs Vgs

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Sw itching 100ms w rite: Current (Amps)

Non-sw itching 100ms w rite: Current (Amps)

Premier II

DriveReturn

Sensor

I2C

BIAS

I2C DACModule


Memory• The properties of ferroelectrics all derive from its

remanent polarization, its memory.

• Ferroelectric materials remember everything that is done to them even during manufacturing.

• For any particular test, the preset condition is all tests and rest periods that preceded!

• Because of memory, every sample continues to change every millisecond, every second, every day, every year.

• To truly understand you’re a sample, you must record its history.


Vision• Because of the memory and aging effects in ferroelectric

materials, Radiant created the Vision test program.

Vision uses a database, called a dataset, to allow you to record the complete history of every test on a sample or every sample in a lot.

Vision can create programs of test tasks that will execute the same way every time they are called to create uniformity in timing and execution.

• You are not using the full power of a Radiant tester unless you create test definitions in the Vision Editor and store the results in datasets in the Vision Archive!


Summary• Radiant’s testers

Are thermodynamic state testers.

Vary one thermodynamic state variable and measure the change in one or more other state variables.

Measure absolute physical parameters directly.

Report the measured parameter, not a model fit.

Are constructed so that the measurement channel has no knowledge of the stimulus.


Summary• Radiant’s testers

Use a triangle wave so that the individual components of a hysteresis loop can be recognized

Measure the following components:− Linear and non-linear capacitance− Remanent polarization− Small signal capacitance− Leakage− Hysteresis in small signal capacitor vs voltage− Hysteresis in leakage vs voltage − Electrode contact diode function− Coupled properties: piezoelectricity, pyroelectricity,

magneto-electricity, and ferroelectric transistor function.


Summary• Non-linear materials remember their history, even the

pattern of their test procedures.

Inconsistent sample histories make measurement precision fuzzy.

• To make precise measurements, control the history of the sample and its test procedures!


Summary

• The Vision operating system that controls the Radiant testers is designed to record and analyze sample history.

Datasets record the execution of programs constructed by the user.

Programs ensure reproducible consistency in test execution.

• Vision is the tester! The hardware was designed to support Vision.

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Characterizing Non-linear Materials

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